Stochastic Discount Factor Models and the Equity Premium Puzzle

Otrok, Christopher and Ravikumar, B and Whiteman, Charles (2001): Stochastic Discount Factor Models and the Equity Premium Puzzle.

Abstract

One view of the equity premium puzzle is that in the standard asset-pricing model with time-separable preferences, the volatility of the stochastic discount factor, for plausible values of risk aversion, is too low to be consistent with consumption and asset return data. We adopt this characterization of the puzzle, due to Hansen and Jagannathan (1991), and establish two results: (i) resolutions of the puzzle based on complete frictionless markets and non-separabilities in preferences are very sensitive to small changes in the consumption data, and (ii) models with frictions avoid this sensitivity problem. Using quarterly data from 1947-97, we calibrate a state non-separable model and a time non-separable model to satisfy the Hansen-Jagannathan volatility bound and show that the two resolutions are not robust. We support our argument via a bootstrap experiment where the models almost always violate the bound. These violations are primarily due to the fact that small changes in consumption growth moments imply changes in the mean of the stochastic discount factor, which render the volatility of the stochastic discount factor to be too low relative to the bound. Asset-pricing models with frictions, however, are much more successful in the bootstrap experiment relative to the case without frictions.

• Item Type: MPRA Paper
• Language: English
• Keywords: Stochastic Discount Factor; Hansen-Jagannathan Bound; Equity Premium
• Subjects: G - Financial Economics > G1 - General Financial Markets > G12 - Asset Pricing ; Trading Volume ; Bond Interest Rates

References

Aiyagari, S. R. and Gertler, M., (1991), “Asset Returns with Transaction Costs and Uninsured Individual Risk,” Journal of Monetary Economics 27: 311-31.

Boldrin, M., L. J. Christiano, and J. D. M. Fisher, (1997), “Habit Persistence and Asset Returns in an Exchange Economy,” Macroeconomic Dynamics 1: 312-332.

Burnside, C., (1994), “Hansen-Jagannathan Bounds as Classical Tests of Asset Pricing Models,” Journal of Business and Economic Statistics 12: 57-79.

Campbell, J. Y., and J. H. Cochrane, (1999), “By Force of Habit: A Consumption-Based Explanation of Aggregate Stock Market Behavior,” Journal of Political Economy, Vol. 107, No. 2, pp. 205-51.

Cecchetti, S. G., P-S. Lam, and N. C. Mark, (1994), “Testing Volatility Restrictions on Intertemporal Marginal Rates of Substitution Implied by Euler Equations and Asset Returns,” Journal of Finance 49: 123-152.

Cochrane, J. H., L. P. Hansen, (1992), “Asset Pricing Explorations for Macroeconomics,” in Olivier J. Blanchard and Stanley Fischer, eds. NBER Macroeconomics Annual 1992 115-163.

Constantinides, G. C., (1990), “Habit Formation: A Resolution of the Equity Premium Puzzle,” Journal of Political Economy 98: 519-43.

Epstein, L. G., and S. E. Zin, (1991), “Substitution, Risk Aversion, and the Temporal Behavior of Consumption and Asset Returns: An Empirical Analysis,” Journal of Political Economy 99: 263-286.

Gregory, A. W., and G. W. Smith, (1992), “Sampling Variability in Hansen-Jagannathan Bounds,” Economics Letters 38: 263-267.

Hansen, L. P., and R. Jagannathan, (1991), “Implications of Security Market Data for Models of Dynamic Economies,” Journal of Political Economy 99: 225-262.

He, H., and D. M. Modest, (1995), “Market Frictions and Consumption-Based Asset Pricing,” Journal of Political Economy 103: 94-117.

Heaton, J. and D. J. Lucas, (1996), “Evaluating the Effects of Incomplete Markets on Risk Sharing and Asset Pricing,” Journal of Political Economy 104: 443-487.

Ljungqvist, L. and T. J. Sargent, 2000. Recursive Macroeconomic Theory. Cambridge: MIT Press.

Lucas, D. J., (1994), “Asset Pricing with Undiversifiable Income Risk and Short Sales Constraints: Deepening the Equity Premium Puzzle,” Journal of Monetary Economics 34: 325-341.

Lucas, R. E. Jr., (1978), “Asset Prices in an Exchange Economy,” Econometrica 46: 1429-1445.

Luttmer, E. G. J., (1996), “Asset Pricing in Economies with Frictions,” Econometrica 64: 1439-1467.

Mehra, R. and E. C. Prescott, (1985), “The Equity Premium: A Puzzle,” Journal of Monetary Economics 15: 145-161.

Otrok, C., B. Ravikumar and C. H. Whiteman, (2002) “Evaluating Asset-Pricing Models Using the Hansen-Jagannathan Bound: A Monte Carlo Investigation” Journal of Applied Econometrics 17: 149-174.

Weil, P., (1989), “The Equity Premium Puzzle and The Risk-Free Rate Puzzle,” Journal of Monetary Economics 24: 401-421.